Reference 2.1. The integral over a finitely additive measure, usually called the Radon integral, is constructed according to the same scheme as the Lebesgue integral over the Lebesgue measure. Its construction is developed in [1]} and also, in a more modern form, in [2]}. Note that if the original space \( X \)  is countable and the measure \( \mu \)  is not countably additive, then the integral on \( X \)  cannot be replaced by a sum (series). Such integrals have other features as well.
